Title: Reconstructing Kernel States via Knowledge-Informed Methods from Heterogeneous Partial Observations

Abstract: In practice, scientific systems are seldom captured through full, uniformly sampled state trajectories. Instead, data typically consists of partial, noisy, and heterogeneous measurements that offer only fragmented glimpses into latent dynamical states. To address this, we present MAAT (Model Aware Approximation of Trajectories), a novel framework designed for knowledge-informed Kernel State Reconstruction within partially observed dynamical systems. MAAT approaches reconstruction within a reproducing kernel Hilbert space, integrating heterogeneous observation operators alongside semantic and structural priors such as non-negativity, conservation constraints, and domain-specific measurement models. This methodology produces smooth, physically consistent state estimates that include analytic time derivatives, thereby establishing a rigorous interface between fragmented measurements and downstream mechanistic discovery techniques like symbolic regression. Evaluations across nine scientific benchmarks, various noise conditions, and a real-world COVID-19 dataset demonstrate that MAAT significantly lowers both trajectory and derivative reconstruction errors compared to robust baseline methods.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC